Probability, Random Variables, and Random Processes (eBook, ePUB)
Theory and Signal Processing Applications
Probability, Random Variables, and Random Processes (eBook, ePUB)
Theory and Signal Processing Applications
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Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: * Several appendices include related…mehr
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- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 794
- Erscheinungstermin: 15. Oktober 2012
- Englisch
- ISBN-13: 9781118393956
- Artikelnr.: 37350369
- Verlag: John Wiley & Sons
- Seitenzahl: 794
- Erscheinungstermin: 15. Oktober 2012
- Englisch
- ISBN-13: 9781118393956
- Artikelnr.: 37350369
e Theorem 540 9.10 Bayes Estimation 542 9.11 Mean-Square-Error Estimation 545 9.12 Mean-Absolute-Error Estimation 552 9.13 Orthogonality Condition 553 9.14 Properties of Estimators 555 9.15 Maximum A Posteriori Estimation 561 9.16 Maximum Likelihood Estimation 567 9.17 Likelihood Ratio Test 569 9.18 Expectation-Maximization Algorithm 570 9.19 Method of Moments 576 9.20 Least-Squares Estimation 577 9.21 Properties of LS Estimators 582 9.22 Best Linear Unbiased Estimation 586 9.23 Properties of BLU Estimators 590 Problems 592 Further Reading 595 A Note on Part III of the Book 595 APPENDICES Introduction to Appendices 597 A Summaries of Univariate Parametric Distributions 599 A.1 Notation 599 A.2 Further Reading 600 A.3 Continuous Random Variables 601 A.4 Discrete Random Variables 623 B Functions and Properties 634 B.1 Continuity and Bounded Variation 634 B.2 Supremum and Infimum 640 B.3 Order Notation 640 B.4 Floor and Ceiling Functions 641 B.5 Convex and Concave Functions 641 B.6 Even and Odd Functions 641 B.7 Signum Function 643 B.8 Dirac Delta Function 644 B.9 Kronecker Delta Function 645 B.10 Unit-Step Functions 646 B.11 Rectangle Functions 647 B.12 Triangle and Ramp Functions 647 B.13 Indicator Functions 648 B.14 Sinc Function 649 B.15 Logarithm Functions 650 B.16 Gamma Functions 651 B.17 Beta Functions 653 B.18 Bessel Functions 655 B.19 Q-Function and Error Functions 655 B.20 Marcum Q-Function 659 B.21 Zeta Function 659 B.22 Rising and Falling Factorials 660 B.23 Laguerre Polynomials 661 B.24 Hypergeometric Functions 662 B.25 Bernoulli Numbers 663 B.26 Harmonic Numbers 663 B.27 Euler-Mascheroni Constant 664 B.28 Dirichlet Function 664 Further Reading 664 C Frequency-Domain Transforms and Properties 665 C.1 Laplace Transform 665 C.2 Continuous-Time Fourier Transform 669 C.3 z-Transform 670 C.4 Discrete-Time Fourier Transform 676 Further Reading 677 D Integration and Integrals 678 D.1 Review of Riemann Integral 678 D.2 Riemann-Stieltjes Integral 681 D.3 Lebesgue Integral 684 D.4 Pdf Integrals 688 D.5 Indefinite and Definite Integrals 690 D.6 Integral Formulas 692 D.7 Double Integrals of Special Functions 692 Further Reading 696 E Identities and Infinite Series 697 E.1 Zero and Infinity 697 E.2 Minimum and Maximum 697 E.3 Trigonometric Identities 698 E.4 Stirling's Formula 698 E.5 Taylor Series 699 E.6 Series Expansions and Closed-Form Sums 699 E.7 Vandermonde's Identity 702 E.8 Pmf Sums and Functional Forms 703 E.9 Completing the Square 704 E.10 Summation by Parts 705 Further Reading 706 F Inequalities and Bounds for Expectations 707 F.1 Cauchy-Schwarz and H
older Inequalities 707 F.2 Triangle and Minkowski Inequalities 708 F.3 Bienaym
e, Chebyshev, and Markov Inequalities 709 F.4 Chernoff's Inequality 711 F.5 Jensen's Inequality 713 F.6 Cram
er-Rao Inequality 714 Further Reading 718 G Matrix and Vector Properties 719 G.1 Basic Properties 719 G.2 Four Fundamental Subspaces 721 G.3 Eigendecomposition 722 G.4 LU, LDU, and Cholesky Decompositions 724 G.5 Jacobian Matrix and the Jacobian 726 G.6 Kronecker and Schur Products 728 G.7 Properties of Trace and Determinant 728 G.8 Matrix Inversion Lemma 729 G.9 Cauchy-Schwarz Inequality 730 G.10 Differentiation 730 G.11 Complex Differentiation 731 Further Reading 732 GLOSSARY 733 REFERENCES 743 INDEX 755 PART III Applications in Signal Processing and Communications Chapters at the Web Site www.wiley.com/go/randomprocesses 10 Communication Systems and Information Theory 771 10.1 Introduction 771 10.2 Transmitter 771 10.3 Transmission Channel 783 10.4 Receiver 786 10.5 Information Theory 803 Problems 821 Further Reading 824 11 Optimal Filtering www.wiley.com/go/randomprocesses 825 11.1 Introduction 825 11.2 Optimal Linear Filtering 825 11.3 Optimal Filter Applications 827 11.4 Noncausal Wiener Filter 829 11.5 Causal Wiener Filter 831 11.6 Prewhitening Filter 837 11.7 FIR Wiener Filter 839 11.8 Kalman Filter 844 11.9 Steady-State Kalman Filter 851 11.10 Linear Predictive Coding 857 11.11 Lattice Prediction-Error Filter 861 11.12 Levinson-Durbin Algorithm 865 11.13 Least-Squares Filtering 868 11.14 Recursive Least-Squares 872 Problems 876 Further Reading 879 12 Adaptive Filtering www.wiley.com/go/randomprocesses 880 12.1 Introduction 880 12.2 MSE Properties 880 12.3 Steepest Descent 889 12.4 Newton's Method 894 12.5 LMS Algorithm 895 12.6 Modified LMS Algorithms 911 12.7 Adaptive IIR Filtering 923 Problems 936 Further Reading 939 13 Equalization, Beamforming, and Direction Finding www.wiley.com/go/randomprocesses 940 13.1 Introduction 940 13.2 Channel Equalization 941 13.3 Optimal Bussgang Algorithm 943 13.4 Blind Equalizer Algorithms 949 13.5 CMA Performance Surface 952 13.6 Antenna Arrays 958 13.7 Beampatterns 960 13.8 Optimal Beamforming 962 13.9 Adaptive Beamforming 970 13.10 Direction Finding 981 Problems 985 Further Reading 989
e Theorem 540 9.10 Bayes Estimation 542 9.11 Mean-Square-Error Estimation 545 9.12 Mean-Absolute-Error Estimation 552 9.13 Orthogonality Condition 553 9.14 Properties of Estimators 555 9.15 Maximum A Posteriori Estimation 561 9.16 Maximum Likelihood Estimation 567 9.17 Likelihood Ratio Test 569 9.18 Expectation-Maximization Algorithm 570 9.19 Method of Moments 576 9.20 Least-Squares Estimation 577 9.21 Properties of LS Estimators 582 9.22 Best Linear Unbiased Estimation 586 9.23 Properties of BLU Estimators 590 Problems 592 Further Reading 595 A Note on Part III of the Book 595 APPENDICES Introduction to Appendices 597 A Summaries of Univariate Parametric Distributions 599 A.1 Notation 599 A.2 Further Reading 600 A.3 Continuous Random Variables 601 A.4 Discrete Random Variables 623 B Functions and Properties 634 B.1 Continuity and Bounded Variation 634 B.2 Supremum and Infimum 640 B.3 Order Notation 640 B.4 Floor and Ceiling Functions 641 B.5 Convex and Concave Functions 641 B.6 Even and Odd Functions 641 B.7 Signum Function 643 B.8 Dirac Delta Function 644 B.9 Kronecker Delta Function 645 B.10 Unit-Step Functions 646 B.11 Rectangle Functions 647 B.12 Triangle and Ramp Functions 647 B.13 Indicator Functions 648 B.14 Sinc Function 649 B.15 Logarithm Functions 650 B.16 Gamma Functions 651 B.17 Beta Functions 653 B.18 Bessel Functions 655 B.19 Q-Function and Error Functions 655 B.20 Marcum Q-Function 659 B.21 Zeta Function 659 B.22 Rising and Falling Factorials 660 B.23 Laguerre Polynomials 661 B.24 Hypergeometric Functions 662 B.25 Bernoulli Numbers 663 B.26 Harmonic Numbers 663 B.27 Euler-Mascheroni Constant 664 B.28 Dirichlet Function 664 Further Reading 664 C Frequency-Domain Transforms and Properties 665 C.1 Laplace Transform 665 C.2 Continuous-Time Fourier Transform 669 C.3 z-Transform 670 C.4 Discrete-Time Fourier Transform 676 Further Reading 677 D Integration and Integrals 678 D.1 Review of Riemann Integral 678 D.2 Riemann-Stieltjes Integral 681 D.3 Lebesgue Integral 684 D.4 Pdf Integrals 688 D.5 Indefinite and Definite Integrals 690 D.6 Integral Formulas 692 D.7 Double Integrals of Special Functions 692 Further Reading 696 E Identities and Infinite Series 697 E.1 Zero and Infinity 697 E.2 Minimum and Maximum 697 E.3 Trigonometric Identities 698 E.4 Stirling's Formula 698 E.5 Taylor Series 699 E.6 Series Expansions and Closed-Form Sums 699 E.7 Vandermonde's Identity 702 E.8 Pmf Sums and Functional Forms 703 E.9 Completing the Square 704 E.10 Summation by Parts 705 Further Reading 706 F Inequalities and Bounds for Expectations 707 F.1 Cauchy-Schwarz and H
older Inequalities 707 F.2 Triangle and Minkowski Inequalities 708 F.3 Bienaym
e, Chebyshev, and Markov Inequalities 709 F.4 Chernoff's Inequality 711 F.5 Jensen's Inequality 713 F.6 Cram
er-Rao Inequality 714 Further Reading 718 G Matrix and Vector Properties 719 G.1 Basic Properties 719 G.2 Four Fundamental Subspaces 721 G.3 Eigendecomposition 722 G.4 LU, LDU, and Cholesky Decompositions 724 G.5 Jacobian Matrix and the Jacobian 726 G.6 Kronecker and Schur Products 728 G.7 Properties of Trace and Determinant 728 G.8 Matrix Inversion Lemma 729 G.9 Cauchy-Schwarz Inequality 730 G.10 Differentiation 730 G.11 Complex Differentiation 731 Further Reading 732 GLOSSARY 733 REFERENCES 743 INDEX 755 PART III Applications in Signal Processing and Communications Chapters at the Web Site www.wiley.com/go/randomprocesses 10 Communication Systems and Information Theory 771 10.1 Introduction 771 10.2 Transmitter 771 10.3 Transmission Channel 783 10.4 Receiver 786 10.5 Information Theory 803 Problems 821 Further Reading 824 11 Optimal Filtering www.wiley.com/go/randomprocesses 825 11.1 Introduction 825 11.2 Optimal Linear Filtering 825 11.3 Optimal Filter Applications 827 11.4 Noncausal Wiener Filter 829 11.5 Causal Wiener Filter 831 11.6 Prewhitening Filter 837 11.7 FIR Wiener Filter 839 11.8 Kalman Filter 844 11.9 Steady-State Kalman Filter 851 11.10 Linear Predictive Coding 857 11.11 Lattice Prediction-Error Filter 861 11.12 Levinson-Durbin Algorithm 865 11.13 Least-Squares Filtering 868 11.14 Recursive Least-Squares 872 Problems 876 Further Reading 879 12 Adaptive Filtering www.wiley.com/go/randomprocesses 880 12.1 Introduction 880 12.2 MSE Properties 880 12.3 Steepest Descent 889 12.4 Newton's Method 894 12.5 LMS Algorithm 895 12.6 Modified LMS Algorithms 911 12.7 Adaptive IIR Filtering 923 Problems 936 Further Reading 939 13 Equalization, Beamforming, and Direction Finding www.wiley.com/go/randomprocesses 940 13.1 Introduction 940 13.2 Channel Equalization 941 13.3 Optimal Bussgang Algorithm 943 13.4 Blind Equalizer Algorithms 949 13.5 CMA Performance Surface 952 13.6 Antenna Arrays 958 13.7 Beampatterns 960 13.8 Optimal Beamforming 962 13.9 Adaptive Beamforming 970 13.10 Direction Finding 981 Problems 985 Further Reading 989